Cargando…
Comparing Brain Networks of Different Size and Connectivity Density Using Graph Theory
Graph theory is a valuable framework to study the organization of functional and anatomical connections in the brain. Its use for comparing network topologies, however, is not without difficulties. Graph measures may be influenced by the number of nodes (N) and the average degree (k) of the network....
Autores principales: | , , |
---|---|
Formato: | Texto |
Lenguaje: | English |
Publicado: |
Public Library of Science
2010
|
Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2965659/ https://www.ncbi.nlm.nih.gov/pubmed/21060892 http://dx.doi.org/10.1371/journal.pone.0013701 |
_version_ | 1782189519927246848 |
---|---|
author | van Wijk, Bernadette C. M. Stam, Cornelis J. Daffertshofer, Andreas |
author_facet | van Wijk, Bernadette C. M. Stam, Cornelis J. Daffertshofer, Andreas |
author_sort | van Wijk, Bernadette C. M. |
collection | PubMed |
description | Graph theory is a valuable framework to study the organization of functional and anatomical connections in the brain. Its use for comparing network topologies, however, is not without difficulties. Graph measures may be influenced by the number of nodes (N) and the average degree (k) of the network. The explicit form of that influence depends on the type of network topology, which is usually unknown for experimental data. Direct comparisons of graph measures between empirical networks with different N and/or k can therefore yield spurious results. We list benefits and pitfalls of various approaches that intend to overcome these difficulties. We discuss the initial graph definition of unweighted graphs via fixed thresholds, average degrees or edge densities, and the use of weighted graphs. For instance, choosing a threshold to fix N and k does eliminate size and density effects but may lead to modifications of the network by enforcing (ignoring) non-significant (significant) connections. Opposed to fixing N and k, graph measures are often normalized via random surrogates but, in fact, this may even increase the sensitivity to differences in N and k for the commonly used clustering coefficient and small-world index. To avoid such a bias we tried to estimate the N,k-dependence for empirical networks, which can serve to correct for size effects, if successful. We also add a number of methods used in social sciences that build on statistics of local network structures including exponential random graph models and motif counting. We show that none of the here-investigated methods allows for a reliable and fully unbiased comparison, but some perform better than others. |
format | Text |
id | pubmed-2965659 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2010 |
publisher | Public Library of Science |
record_format | MEDLINE/PubMed |
spelling | pubmed-29656592010-11-08 Comparing Brain Networks of Different Size and Connectivity Density Using Graph Theory van Wijk, Bernadette C. M. Stam, Cornelis J. Daffertshofer, Andreas PLoS One Research Article Graph theory is a valuable framework to study the organization of functional and anatomical connections in the brain. Its use for comparing network topologies, however, is not without difficulties. Graph measures may be influenced by the number of nodes (N) and the average degree (k) of the network. The explicit form of that influence depends on the type of network topology, which is usually unknown for experimental data. Direct comparisons of graph measures between empirical networks with different N and/or k can therefore yield spurious results. We list benefits and pitfalls of various approaches that intend to overcome these difficulties. We discuss the initial graph definition of unweighted graphs via fixed thresholds, average degrees or edge densities, and the use of weighted graphs. For instance, choosing a threshold to fix N and k does eliminate size and density effects but may lead to modifications of the network by enforcing (ignoring) non-significant (significant) connections. Opposed to fixing N and k, graph measures are often normalized via random surrogates but, in fact, this may even increase the sensitivity to differences in N and k for the commonly used clustering coefficient and small-world index. To avoid such a bias we tried to estimate the N,k-dependence for empirical networks, which can serve to correct for size effects, if successful. We also add a number of methods used in social sciences that build on statistics of local network structures including exponential random graph models and motif counting. We show that none of the here-investigated methods allows for a reliable and fully unbiased comparison, but some perform better than others. Public Library of Science 2010-10-28 /pmc/articles/PMC2965659/ /pubmed/21060892 http://dx.doi.org/10.1371/journal.pone.0013701 Text en van Wijk et al. http://creativecommons.org/licenses/by/4.0/ This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited. |
spellingShingle | Research Article van Wijk, Bernadette C. M. Stam, Cornelis J. Daffertshofer, Andreas Comparing Brain Networks of Different Size and Connectivity Density Using Graph Theory |
title | Comparing Brain Networks of Different Size and Connectivity Density Using Graph Theory |
title_full | Comparing Brain Networks of Different Size and Connectivity Density Using Graph Theory |
title_fullStr | Comparing Brain Networks of Different Size and Connectivity Density Using Graph Theory |
title_full_unstemmed | Comparing Brain Networks of Different Size and Connectivity Density Using Graph Theory |
title_short | Comparing Brain Networks of Different Size and Connectivity Density Using Graph Theory |
title_sort | comparing brain networks of different size and connectivity density using graph theory |
topic | Research Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2965659/ https://www.ncbi.nlm.nih.gov/pubmed/21060892 http://dx.doi.org/10.1371/journal.pone.0013701 |
work_keys_str_mv | AT vanwijkbernadettecm comparingbrainnetworksofdifferentsizeandconnectivitydensityusinggraphtheory AT stamcornelisj comparingbrainnetworksofdifferentsizeandconnectivitydensityusinggraphtheory AT daffertshoferandreas comparingbrainnetworksofdifferentsizeandconnectivitydensityusinggraphtheory |